Terminology and notation |
Introduction |
Infinitesimal deformations / 1: |
Extensions / 1.1: |
Generalities / 1.1.1: |
Extensions of schemes / 1.1.2: |
Locally trivial deformations / 1.2: |
Generalities on deformations / 1.2.1: |
Infinitesimal deformations of nonsingular affine schemes / 1.2.2: |
Extending automorphisms of deformations / 1.2.3: |
First-order locally trivial deformations / 1.2.4: |
Higher-order deformations - obstructions / 1.2.5: |
Formal deformation theory / 2: |
Obstructions / 2.1: |
Functors of Artin rings / 2.2: |
The theorem of Schlessinger / 2.3: |
The local moduli functors / 2.4: |
Obstruction spaces / 2.4.1: |
Algebraic surfaces / 2.4.3: |
Formal versus algebraic deformations / 2.5: |
Automorphisms and prorepresentability / 2.6: |
The automorphism functor / 2.6.1: |
Isotriviality / 2.6.2: |
Examples of deformation functors / 3: |
Affine schemes / 3.1: |
First-order deformations / 3.1.1: |
The second cotangent module and obstructions / 3.1.2: |
Comparison with deformations of the nonsingular locus / 3.1.3: |
Quotient singularities / 3.1.4: |
Closed subschemes / 3.2: |
The local Hilbert functor / 3.2.1: |
The forgetful morphism / 3.2.2: |
The local relative Hilbert functor / 3.2.4: |
Invertible sheaves / 3.3: |
The local Picard functors / 3.3.1: |
Deformations of sections, I / 3.3.2: |
Deformations of pairs (X, L) / 3.3.3: |
Deformations of sections, II / 3.3.4: |
Morphisms / 3.4: |
Deformations of a morphism leaving domain and target fixed / 3.4.1: |
Deformations of a morphism leaving the target fixed / 3.4.2: |
Morphisms from a nonsingular curve with fixed target / 3.4.3: |
Deformations of a closed embedding / 3.4.4: |
Stability and costability / 3.4.5: |
Hilbert and Quot schemes / 4: |
Castelnuovo-Mumford regularity / 4.1: |
Flatness in the projective case / 4.2: |
Flatness and Hilbert polynomials / 4.2.1: |
Stratifications / 4.2.2: |
Flattening stratifications / 4.2.3: |
Hilbert schemes / 4.3: |
Linear systems / 4.3.1: |
Grassmannians / 4.3.3: |
Existence / 4.3.4: |
Quot schemes / 4.4: |
Local properties / 4.4.1: |
Flag Hilbert schemes / 4.5: |
Examples and applications / 4.5.1: |
Complete intersections / 4.6.1: |
An obstructed (nonreduced) scheme / 4.6.2: |
Relative grassmannians and projective bundles / 4.6.4: |
Hilbert schemes of points / 4.6.5: |
Schemes of morphisms / 4.6.6: |
Focal loci / 4.6.7: |
Plane curves / 4.7: |
Equisingular infinitesimal deformations / 4.7.1: |
The Severi varieties / 4.7.2: |
Nonemptiness of Severi varieties / 4.7.3: |
Flatness / A: |
Differentials / B: |
Smoothness / C: |
Regular embeddings / D: |
Relative complete intersection morphisms / D.2: |
Functorial language / E: |
References |
List of symbols |
Index |
Terminology and notation |
Introduction |
Infinitesimal deformations / 1: |